Understanding fractions (age 10+)

Question 1

Jamie wants to make 3 batches of pancake mix. Each batch uses 2/5 cup of milk. Which choice correctly shows the algebraic equation for the total milk needed and a correct description of a bar model that represents the situation?

Accepted Answer

Equation: total = 3 × (2/5) = 6/5 cups. Bar model: three identical bars, each divided into 5 equal parts with 2 parts shaded; together the shaded parts make 6 of the 5 parts (one whole bar plus one extra part).

Answer

Equation: total = 3 + (2/5) = 17/5 cups. Bar model: three whole bars and, on a fourth bar, 2 of the 5 parts are shaded.

Answer

Equation: total = (2/5) ÷ 3 = 2/15 cups. Bar model: one bar divided into 5 parts, 2 parts shaded, then the whole bar is split into 3 equal sections.

Answer

Equation: total = 3 × (5/2) = 15/2 cups. Bar model: three bars, each divided into 2 parts with 5 parts shaded on each bar.

Question 2

Lila is preparing lemonade for a school event. She needs to fill 4 identical jars, and each jar requires 3/8 liter of lemon juice. Which option shows the correct algebraic equation for the total amount of lemon juice needed and correctly describes a bar model that represents this situation?

Accepted Answer

Equation: 4 × 3/8 = total lemon juice. Bar model: Four separate bars, each divided into 8 equal parts with 3 parts shaded; the shaded parts from all four bars together show the total.

Answer

Equation: 3/8 × 4 = 3/2 liters. Bar model: Three bars, each divided into 8 parts with 4 parts shaded.

Answer

Equation: 4 × 3/8 = 12/8 liters. Bar model: A single bar divided into 8 equal parts with 12 parts shaded.

Answer

Equation: 4 + 3/8 = total lemon juice. Bar model: One whole bar representing 4 liters plus a small bar divided into 8 parts with 3 shaded.

Question 3

At the end of the school art project, the class of 25 students counted that 7 students drew a mandala. The teacher wants to show this result in three ways: 1. as a fraction of the whole class, 2. as a percentage of the whole class, and 3. by shading the appropriate portion of a pie chart. Which of the following shows all three representations correctly?

Accepted Answer

Fraction 7/25, percent 28%, pie chart with 28% of the circle shaded.

Answer

Fraction 7/25, percent 35%, pie chart with 35% of the circle shaded.

Answer

Fraction 25/7, percent 25%, pie chart with 25% of the circle shaded.

Answer

Fraction 7/25, percent 70%, pie chart with 70% of the circle shaded.

Try three questions

Jamie wants to make 3 batches of pancake mix. Each batch uses 2/5 cup of milk. Which choice correctly shows the algebraic equation for the total milk needed and a correct description of a bar model that represents the situation?

Lila is preparing lemonade for a school event. She needs to fill 4 identical jars, and each jar requires 3/8 liter of lemon juice. Which option shows the correct algebraic equation for the total amount of lemon juice needed and correctly describes a bar model that represents this situation?

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